Structural Concrete - Hassoun

732 Chapter 19 Introduction to Prestressed Concrete
Partially prestressed concrete can be considered an intermediate form between reinforced and
fully prestressed concrete. In reinforced concrete members, cracks develop under working loads;
therefore, reinforcement is placed in the tension zone. In prestressed concrete members, cracks do
not usually develop under working loads. The compressive stresses due to prestressing may equal
or exceed the tensile stresses due to external loadings. Therefore, a partially prestressed concrete
member may be considered a reinforced concrete member in which internal stresses are introduced
to counteract part of the stress from external loadings so that tensile stresses in the concrete do
not exceed a limited value under working load. It reduces to reinforced concrete when no internal
stresses act on the member. Full prestressing is an upper extreme of partial prestressing in which
nonprestressed reinforcing steel reduces to 0.
Prestressing jack with a load cell.
Between a reinforced cracked member and a fully prestressed uncracked member, there exists
a wide range of design in partial prestressing (Fig. 19.3). A proper choice of the degree of prestressing
will produce a safe and economical structure.
Figure 19.3 shows the load–deflection curves of concrete beams containing different amounts
and types of reinforcement. Curve a represents a reinforced concrete beam, which normally cracks
at a small load W cr . The cracking moment M cr can be determined as follows:
M cr = f rI
c
where
f r = modulus of rupture of concrete = 7.5λ √ f c
′
I = moment of inertia of gross concrete section
c = distance from neutral axis to tensile extreme fibers
The cracking load can be determined from the cracking moment when the span and the type
of loading are specified. For a simply supported beam subjected to a concentrated load at midspan,
W cr = (4M cr )/L.
Curves e and f represent underreinforced and overreinforced fully prestressed concrete beams,
respectively. The overreinforced concrete beam fails by crushing of the concrete before the steel